Weighted Divergent Beam Ray Transform: Reconstruction, Unique continuation and Stability

In this article, we establish that any symmetric \(m\)-tensor field can be recovered pointwise from partial data of the \(k\)-th weighted divergent ray transform for any \(k \in \mathbb{Z}^{+} \cup\{0\}\). Using the unique continuation property of the fractional Laplacian, we further prove the unique continuation of the fractional divergent beam ray transform for both vector fields and symmetric 2-tensor fields. Additionally, we derive explicit reconstruction formulas and stability results for vector fields and symmetric 2-tensor fields in terms of fractional divergent beam ray transform data. Finally, we conclude by proving a unique continuation result for the divergent beam ray transform for functions.